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Question -

Under certain circumstances, a nucleus candecay by emitting a particle more massive than an α-particle. Consider thefollowing decay processes:

Calculate the Q-values for thesedecays and determine that both are energetically allowed.



Answer -

Take a  emission nuclear reaction:

 

We know that:

Mass of m1 = 223.01850 u
Mass of m2 = 208.98107 u
Mass ofm3 = 14.00324 u

Hence, the Q-value of thereaction is given as:

Q = (m1 − m2 − m3c2

= (223.01850 − 208.98107 − 14.00324) c2

= (0.03419 c2) u

But 1 u = 931.5 MeV/c2

Q = 0.03419 ×931.5

= 31.848 MeV

Hence, the Q-value of the nuclearreaction is 31.848 MeV. Since the value is positive, the reaction isenergetically allowed.

Now take a emission nuclear reaction:

We know that:

Mass of m1 = 223.01850
Mass of m2 = 219.00948
Mass ofm3 = 4.00260

Q-value of this nuclear reaction isgiven as:

Q = (m1 − m2 − m3c2

= (223.01850 − 219.00948 − 4.00260) C2

= (0.00642 c2) u

= 0.00642 × 931.5 = 5.98 MeV

Hence, the Q value of thesecond nuclear reaction is 5.98 MeV. Since the value is positive, the reactionis energetically allowed.

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